TSTP Solution File: SET587^5 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SET587^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue May 21 03:03:00 EDT 2024

% Result   : Theorem 8.27s 2.82s
% Output   : Refutation 8.27s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   76 (   7 unt;   8 typ;   0 def)
%            Number of atoms       :  279 (  50 equ;   0 cnn)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  487 ( 121   ~;  99   |;  27   &; 227   @)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    9 (   9   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   10 (   7 usr;   6 con; 0-2 aty)
%            Number of variables   :   81 (  40   ^  41   !;   0   ?;  81   :)

% Comments : 
%------------------------------------------------------------------------------
thf(a_type,type,
    a: $tType ).

thf(sk1_type,type,
    sk1: a > $o ).

thf(sk2_type,type,
    sk2: a > $o ).

thf(sk3_type,type,
    sk3: a ).

thf(sk4_type,type,
    sk4: a ).

thf(sk5_type,type,
    sk5: a > a ).

thf(sk6_type,type,
    sk6: a ).

thf(sk8_type,type,
    sk8: a ).

thf(1,conjecture,
    ! [A: a > $o,B: a > $o] :
      ( ( ( ^ [C: a] :
              ( ( A @ C )
              & ~ ( B @ C ) ) )
        = ( ^ [C: a] : $false ) )
      = ( ! [C: a] :
            ( ( A @ C )
           => ( B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_45_pme) ).

thf(2,negated_conjecture,
    ~ ! [A: a > $o,B: a > $o] :
        ( ( ( ^ [C: a] :
                ( ( A @ C )
                & ~ ( B @ C ) ) )
          = ( ^ [C: a] : $false ) )
        = ( ! [C: a] :
              ( ( A @ C )
             => ( B @ C ) ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(3,plain,
    ~ ! [A: a > $o,B: a > $o] :
        ( ( ( ^ [C: a] :
                ( ( A @ C )
                & ~ ( B @ C ) ) )
          = ( ^ [C: a] : $false ) )
        = ( ! [C: a] :
              ( ( A @ C )
             => ( B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(4,plain,
    ( ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) )
   != ( ! [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) ) ) ),
    inference(cnf,[status(esa)],[3]) ).

thf(5,plain,
    ( ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) )
   != ( ! [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) ) ) ),
    inference(lifteq,[status(thm)],[4]) ).

thf(6,plain,
    ( ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
     != ( ^ [A: a] : $false ) )
    | ~ ! [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(8,plain,
    ( ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
     != ( ^ [A: a] : $false ) )
    | ~ ! [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) ) ),
    inference(lifteq,[status(thm)],[6]) ).

thf(10,plain,
    ( ~ ( sk2 @ sk3 )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
     != ( ^ [A: a] : $false ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(11,plain,
    ( ( sk1 @ sk3 )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
     != ( ^ [A: a] : $false ) ) ),
    inference(cnf,[status(esa)],[8]) ).

thf(31,plain,
    ( ( ( sk1 @ sk6 )
      & ~ ( sk2 @ sk6 ) )
    | ( sk1 @ sk3 ) ),
    inference(func_ext,[status(esa)],[11]) ).

thf(35,plain,
    ( ( sk1 @ sk3 )
    | ( sk1 @ sk6 ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(7,plain,
    ( ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) )
    | ! [A: a] :
        ( ( sk1 @ A )
       => ( sk2 @ A ) ) ),
    inference(bool_ext,[status(thm)],[5]) ).

thf(9,plain,
    ( ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) )
    | ! [A: a] :
        ( ( sk1 @ A )
       => ( sk2 @ A ) ) ),
    inference(lifteq,[status(thm)],[7]) ).

thf(12,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A )
      | ( ( ^ [B: a] :
              ( ( sk1 @ B )
              & ~ ( sk2 @ B ) ) )
        = ( ^ [B: a] : $false ) ) ),
    inference(cnf,[status(esa)],[9]) ).

thf(50,plain,
    ! [A: a] :
      ( ( sk1 @ sk3 )
      | ( sk2 @ A )
      | ( ( ^ [B: a] :
              ( ( sk1 @ B )
              & ~ ( sk2 @ B ) ) )
        = ( ^ [B: a] : $false ) )
      | ( ( sk1 @ sk6 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[35,12]) ).

thf(51,plain,
    ( ( sk1 @ sk3 )
    | ( sk2 @ sk6 )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) ) ),
    inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( sk6 ))]]) ).

thf(75,plain,
    ( ( sk1 @ sk3 )
    | ( sk2 @ sk6 )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
     != ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[51,11]) ).

thf(76,plain,
    ( ( sk1 @ sk3 )
    | ( sk2 @ sk6 ) ),
    inference(pattern_uni,[status(thm)],[75:[]]) ).

thf(34,plain,
    ( ( sk1 @ sk3 )
    | ~ ( sk2 @ sk6 ) ),
    inference(cnf,[status(esa)],[31]) ).

thf(92,plain,
    ( ( sk1 @ sk3 )
    | ( ( sk2 @ sk6 )
     != ( sk2 @ sk6 ) ) ),
    inference(paramod_ordered,[status(thm)],[76,34]) ).

thf(93,plain,
    sk1 @ sk3,
    inference(pattern_uni,[status(thm)],[92:[]]) ).

thf(24,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A )
      | ~ ! [B: a] :
            ( ( sk1 @ B )
           => ( sk2 @ B ) )
      | ( ( ^ [B: a] :
              ( ( sk1 @ B )
              & ~ ( sk2 @ B ) ) )
       != ( ^ [B: a] :
              ( ( sk1 @ B )
              & ~ ( sk2 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,5]) ).

thf(25,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A )
      | ~ ! [B: a] :
            ( ( sk1 @ B )
           => ( sk2 @ B ) ) ),
    inference(pattern_uni,[status(thm)],[24:[]]) ).

thf(29,plain,
    ! [A: a] :
      ( ~ ( sk2 @ ( sk5 @ A ) )
      | ( sk2 @ A )
      | ~ ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(292,plain,
    ! [A: a] :
      ( ~ ( sk2 @ ( sk5 @ A ) )
      | ( sk2 @ A )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,29]) ).

thf(293,plain,
    ( ~ ( sk2 @ ( sk5 @ sk3 ) )
    | ( sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( sk3 ))]]) ).

thf(23,plain,
    ! [B: a,A: a] :
      ( ~ ( ( sk1 @ B )
          & ~ ( sk2 @ B ) )
      | ~ ( sk1 @ A )
      | ( sk2 @ A ) ),
    inference(func_ext,[status(esa)],[12]) ).

thf(28,plain,
    ! [B: a,A: a] :
      ( ( sk2 @ A )
      | ~ ( sk1 @ A )
      | ~ ( sk1 @ B )
      | ( sk2 @ B ) ),
    inference(cnf,[status(esa)],[23]) ).

thf(13,plain,
    ( ( ( sk1 @ sk4 )
      & ~ ( sk2 @ sk4 ) )
    | ~ ( sk2 @ sk3 ) ),
    inference(func_ext,[status(esa)],[10]) ).

thf(14,plain,
    ( ~ ( sk2 @ sk3 )
    | ~ ( sk2 @ sk4 ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(117,plain,
    ! [B: a,A: a] :
      ( ( sk2 @ A )
      | ~ ( sk1 @ A )
      | ~ ( sk1 @ B )
      | ~ ( sk2 @ sk4 )
      | ( ( sk2 @ B )
       != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[28,14]) ).

thf(118,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      | ~ ( sk1 @ A )
      | ~ ( sk1 @ sk3 )
      | ~ ( sk2 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).

thf(208,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      | ~ ( sk1 @ A )
      | ~ $true
      | ~ ( sk2 @ sk4 ) ),
    inference(rewrite,[status(thm)],[118,93]) ).

thf(209,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      | ~ ( sk1 @ A )
      | ~ ( sk2 @ sk4 ) ),
    inference(simp,[status(thm)],[208]) ).

thf(211,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      | ~ ( sk2 @ sk4 )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,209]) ).

thf(212,plain,
    ( ( sk2 @ sk3 )
    | ~ ( sk2 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( sk3 ))]]) ).

thf(183,plain,
    ! [A: a] :
      ( ( sk2 @ A )
      | ( ( ^ [B: a] :
              ( ( sk1 @ B )
              & ~ ( sk2 @ B ) ) )
        = ( ^ [B: a] : $false ) )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,12]) ).

thf(184,plain,
    ( ( sk2 @ sk3 )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
      = ( ^ [A: a] : $false ) ) ),
    inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( sk3 ))]]) ).

thf(190,plain,
    ( ( sk2 @ sk3 )
    | ~ ! [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) )
    | ( ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) )
     != ( ^ [A: a] :
            ( ( sk1 @ A )
            & ~ ( sk2 @ A ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[184,5]) ).

thf(191,plain,
    ( ( sk2 @ sk3 )
    | ~ ! [A: a] :
          ( ( sk1 @ A )
         => ( sk2 @ A ) ) ),
    inference(pattern_uni,[status(thm)],[190:[]]) ).

thf(200,plain,
    ( ( sk1 @ sk8 )
    | ( sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[191]) ).

thf(16,plain,
    ( ~ ( sk2 @ sk3 )
    | ( ( sk2 @ sk4 )
     != ( sk2 @ sk3 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[14]) ).

thf(18,plain,
    ( ~ ( sk2 @ sk3 )
    | ( sk4 != sk3 ) ),
    inference(simp,[status(thm)],[16]) ).

thf(243,plain,
    ( ( sk1 @ sk8 )
    | ( sk4 != sk3 )
    | ( ( sk2 @ sk3 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[200,18]) ).

thf(244,plain,
    ( ( sk1 @ sk8 )
    | ( sk4 != sk3 ) ),
    inference(pattern_uni,[status(thm)],[243:[]]) ).

thf(17,plain,
    ( ~ ( sk2 @ sk3 )
    | ( ( sk2 @ sk4 )
     != ( sk2 @ sk3 ) ) ),
    inference(simp,[status(thm)],[16]) ).

thf(26,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A )
      | ~ ( sk2 @ sk3 )
      | ( ( ^ [B: a] :
              ( ( sk1 @ B )
              & ~ ( sk2 @ B ) ) )
       != ( ^ [B: a] :
              ( ( sk1 @ B )
              & ~ ( sk2 @ B ) ) ) ) ),
    inference(paramod_ordered,[status(thm)],[12,10]) ).

thf(27,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ( sk2 @ A )
      | ~ ( sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[26:[]]) ).

thf(38,plain,
    ! [A: a] :
      ( ~ ( sk1 @ A )
      | ~ ( sk2 @ sk3 )
      | ( ( sk2 @ A )
       != ( sk2 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[27,14]) ).

thf(39,plain,
    ( ~ ( sk1 @ sk4 )
    | ~ ( sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk4 ))]]) ).

thf(15,plain,
    ( ~ ( sk2 @ sk3 )
    | ( sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[13]) ).

thf(249,plain,
    ( ( sk1 @ sk8 )
    | ( sk1 @ sk4 )
    | ( ( sk2 @ sk3 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[200,15]) ).

thf(250,plain,
    ( ( sk1 @ sk8 )
    | ( sk1 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[249:[]]) ).

thf(341,plain,
    ( ( sk1 @ sk4 )
    | ( ( sk1 @ sk8 )
     != ( sk1 @ sk4 ) )
    | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[250]) ).

thf(345,plain,
    ( ( sk1 @ sk4 )
    | ( sk8 != sk4 ) ),
    inference(simp,[status(thm)],[341]) ).

thf(30,plain,
    ! [A: a] :
      ( ( sk1 @ ( sk5 @ A ) )
      | ( sk2 @ A )
      | ~ ( sk1 @ A ) ),
    inference(cnf,[status(esa)],[25]) ).

thf(246,plain,
    ( ( sk1 @ sk8 )
    | ~ ( sk2 @ sk4 )
    | ( ( sk2 @ sk3 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[200,14]) ).

thf(247,plain,
    ( ( sk1 @ sk8 )
    | ~ ( sk2 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[246:[]]) ).

thf(356,plain,
    ( ( sk8 != sk4 )
    | ~ ( sk2 @ sk3 )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[345,39]) ).

thf(357,plain,
    ( ( sk8 != sk4 )
    | ~ ( sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[356:[]]) ).

thf(422,plain,
    ! [A: a] :
      ( ( sk1 @ ( sk5 @ A ) )
      | ( sk2 @ A )
      | ( ( sk1 @ sk3 )
       != ( sk1 @ A ) ) ),
    inference(paramod_ordered,[status(thm)],[93,30]) ).

thf(423,plain,
    ( ( sk1 @ ( sk5 @ sk3 ) )
    | ( sk2 @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( sk3 ))]]) ).

thf(240,plain,
    ( ( sk1 @ sk8 )
    | ~ ( sk1 @ sk4 )
    | ( ( sk2 @ sk3 )
     != ( sk2 @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[200,39]) ).

thf(241,plain,
    ( ( sk1 @ sk8 )
    | ~ ( sk1 @ sk4 ) ),
    inference(pattern_uni,[status(thm)],[240:[]]) ).

thf(199,plain,
    ( ~ ( sk2 @ sk8 )
    | ( sk2 @ sk3 ) ),
    inference(cnf,[status(esa)],[191]) ).

thf(358,plain,
    ( ( sk8 != sk4 )
    | ( sk1 @ sk8 )
    | ( ( sk1 @ sk4 )
     != ( sk1 @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[345,241]) ).

thf(359,plain,
    ( ( sk8 != sk4 )
    | ( sk1 @ sk8 ) ),
    inference(pattern_uni,[status(thm)],[358:[]]) ).

thf(580,plain,
    $false,
    inference(e,[status(thm)],[10,293,28,212,244,17,12,39,345,209,18,250,30,5,247,14,184,357,93,29,423,27,3,241,199,359,15,200]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SET587^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n014.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Mon May 20 13:01:39 EDT 2024
% 0.14/0.35  % CPUTime  : 
% 0.82/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.08/0.98  % [INFO] 	 Parsing done (115ms). 
% 1.08/0.98  % [INFO] 	 Running in sequential loop mode. 
% 1.62/1.24  % [INFO] 	 eprover registered as external prover. 
% 1.62/1.24  % [INFO] 	 cvc4 registered as external prover. 
% 1.62/1.25  % [INFO] 	 Scanning for conjecture ... 
% 1.75/1.32  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 1.75/1.34  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 1.75/1.34  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 1.75/1.34  % [INFO] 	 Type checking passed. 
% 1.75/1.34  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 8.27/2.82  % External prover 'e' found a proof!
% 8.27/2.82  % [INFO] 	 Killing All external provers ... 
% 8.27/2.82  % Time passed: 2320ms (effective reasoning time: 1834ms)
% 8.27/2.82  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.27/2.82  % Axioms used in derivation (0): 
% 8.27/2.82  % No. of inferences in proof: 68
% 8.27/2.82  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2320 ms resp. 1834 ms w/o parsing
% 8.27/2.86  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.27/2.86  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------